CN114978195A - Method and system for searching error pattern set related to polar code serial offset list decoding code words - Google Patents

Method and system for searching error pattern set related to polar code serial offset list decoding code words Download PDF

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CN114978195A
CN114978195A CN202210469858.7A CN202210469858A CN114978195A CN 114978195 A CN114978195 A CN 114978195A CN 202210469858 A CN202210469858 A CN 202210469858A CN 114978195 A CN114978195 A CN 114978195A
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error pattern
error
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CN114978195B (en
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赵延龙
尹振东
吴芝路
刘庆之
徐铭栋
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Harbin Institute of Technology
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    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
    • H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
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Abstract

A method and a system for searching an error pattern set related to a polar code serial offset list decoding code word relate to the technical field of polar code decoding and are used for solving the problem that error patterns are omitted when the code word of the conventional Chase-II algorithm is generated. The invention carries out error pattern search for the Rate-1 and SPC outer code corresponding to the polar code serial offset list decoding according to the following processes: the iteration cycle is repeated for many times, and the error pattern epsilon to be selected is obtained by cycle traversal in the error pattern set to be selected during each cycle e Or epsilon with the total number of elements being even/odd e (ii) a Circularly traversing in the error pattern set to be compared to obtain the error pattern epsilon to be compared t Or epsilon with the total number of elements being even/odd t (ii) a For epsilon e And epsilon t Making a conditional decision to determine whether a relationship exists
Figure DDA0003626064760000011
Making other condition decision according to the size of the list to finally determine the error diagramAnd (5) sampling. The invention generates the required error pattern according to the limitation of the input likelihood value sequence length and the list size to the error pattern, and improves the error correction capability of the error pattern in the fast serial offset list decoding application.

Description

Method and system for searching error pattern set related to polar code serial offset list decoding code words
Technical Field
The invention relates to the technical field of polar code decoding, in particular to a polar code serial offset list decoding code word related error pattern set searching method and system.
Background
Compared with the traditional linear block code or other coding modes, the polar code firstly proves that the polar code can reach the channel capacity derived by Shannon in the binary erasure channel under the condition of unlimited code length [1] 。
The polar code rapid serial offset list decoding algorithm is used for rapidly operating the external codes corresponding to different sub binary trees in a decoding binary tree without traversing to each leaf node, so that the calculation amount is saved, and the decoding delay is reduced [2-3] . Existing Chase-II algorithm [4] The method is used for processing the Rate-1 and SPC external codes corresponding to the polar code fast serial offset list decoding algorithm, directly generating a related code word set to be selected and corresponding path reliability measurement according to different error patterns of codebooks corresponding to the two external codes in the decoding process, finally uniformly selecting the most reliable L code words in the path measurement, and selecting the output code words corresponding to the current external code and the corresponding L paths. However, the error pattern generated by the conventional Chase-II algorithm for the Rate-1 and SPC outer codes cannot completely cover the input length N v And the list size is all reliable code words selected by L, and the method can cause the loss of the error correction capability of the original polar code serial offset list decoding algorithm, thereby causing the increase of the block error rate of the communication system.
Disclosure of Invention
In view of the above problems, the present invention provides a method and a system for searching an error pattern set related to a decoding codeword of a polar code serial cancellation list, so as to solve the problem of error pattern omission generated during the generation of a codeword of the conventional Chase-II algorithm.
According to an aspect of the present invention, there is provided a method for searching an error pattern set related to a decoding codeword of a polar code serial cancellation list, for two corresponding external codes of the polar code serial cancellation list decoding: and (3) carrying out error pattern search by the Rate-1 and SPC outer codes according to the following method:
initialization: available error pattern set
Figure BDA0003626064740000011
Unusable sets of error patterns
Figure BDA0003626064740000012
For arbitrary candidate error patterns
Figure BDA0003626064740000013
All have numEp (epsilon) e ) 0; wherein, a l ＝(a l [1],a l [2],...,a l [N v ]) Position coordinates in ascending order of likelihood absolute values representing a sequence of input likelihood values, N v Representing the length of the input sequence of likelihood values; numEp (ε) e ) Is defined as a relation ratio epsilon e The number of small error patterns;
so that the cyclic variable i is stepped from 1 to log 2 (L), L is the total number of paths, each cycle is i +1, and the method is executed according to the following steps in each cycle:
step 1, a candidate error pattern set
Figure BDA0003626064740000021
For the Rate-1 outer code: circularly traversing in the set epSet to obtain a candidate error pattern epsilon e ；
For SPC outer code, when the parity check value p of the likelihood value hard decision result is 0, circularly traversing in the set epSet to obtain the candidate error pattern epsilon with the total number of elements of the candidate error pattern being even number e ；
For SPC outer code, when the parity check value p of the likelihood value hard decision result is 1, circularly traversing in the set epSet to obtain the candidate error pattern epsilon with the total number of elements of the candidate error pattern being odd number e ；
Step 2, the sets of error patterns to be compared
Figure BDA0003626064740000022
ε t Indicating that the error patterns are to be compared,
for a Rate-1 outer code: circularly traversing in the set epCompSet to obtain an error pattern epsilon to be compared t ；
For SPC outer code, when the parity check value p of the likelihood value hard decision result is 0, circularly traversing in the set epCompSet to obtain the error pattern epsilon to be compared, wherein the total number of elements of the error pattern to be compared is even t ；
For SPC outer code, when the parity check value p of the likelihood value hard decision result is 1, circularly traversing in the set epCompSet to obtain the error pattern epsilon to be compared, wherein the total number of elements of the error pattern to be compared is odd number t ；
Step 3, obtaining the candidate error pattern epsilon e And error pattern epsilon to be compared t Making a conditional relationship determination to determine if a relationship epsilon exists t ＜ε e If yes, executing step 4; if not, executing step 2;
step 4, judging whether epsilon exists t E.g. badSet or epsilon t E goodSet and numEp (ε) t ) Not less than L-1, if yes, executing step 5; if not, numEp (ε) e )＝numEp(ε e ) +1, go to step 2; wherein, numEp (ε) t ) Is defined as a relation ratio epsilon t The number of small error patterns;
step 5, if numEp (ε) e )<L, then goodSet ═ goodSet @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }; completing one cycle;
in the cycle log 2 (L) ending the circulation to obtain all the error patterns epsilon to be selected which satisfy the conditions in each circulation e A set of goodSet;
the error pattern set corresponding to the Rate-1 outer code is: goodSet { { a { (a) } { (a) } U { (a) } C l [1],a l [2],...,a l [1+log 2 L]}}；
SPC outer code: if the parity value p is 0, if 1+ log 2 L is odd number, corresponding to errorThe pattern set is goodSet; if 1+ log 2 L is an even number, and the corresponding set of error patterns is: goodSet { { a { (a) } { (a) } U { (a) } C l [1],a l [2],...,a l [1+log 2 L]}}；
SPC outer code: if the parity value p is 1, if 1+ log 2 L is an even number, and the corresponding error pattern set is goodSet; if 1+ log 2 L is an odd number, and the corresponding set of error patterns is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}}。
Further, the parity value p represents a modulo-2 sum of all bits of the path input likelihood value sequence hard decision result sequence, and the calculation formula is as follows:
Figure BDA0003626064740000031
wherein alpha is l [i]Representing the input likelihood value sequence alpha corresponding to the ith path l H (·) represents a hard decision function that makes a decision on the input likelihood value sequence corresponding to the current path l;
Figure BDA0003626064740000032
representing modulo-2 addition.
Further, in step 2 it is determined whether a relationship exists
Figure BDA0003626064740000033
The condition (2) is determined as: satisfy one of the following three conditions
Figure BDA0003626064740000034
Establishing;
A) if ε t |＝|ε e |，|ε t Denotes the set ε t Number of elements, | epsilon e I denotes the set ε e The number of elements of (1) is then epsilon t The absolute value order of likelihood values corresponding to the m-th element is less than epsilon e The absolute value order of the likelihood values corresponding to the mth element;
B) if ε t |＜|ε e If need to satisfy
Figure BDA0003626064740000035
C) If ε t |＜|ε e If there is an error pattern epsilon k To satisfy
Figure BDA0003626064740000036
And is
Figure BDA0003626064740000037
According to another aspect of the present invention, there is provided a polar code serial cancellation list decoding codeword-related error pattern set searching system, comprising:
the device comprises a Rate-1 outer code error pattern searching module, a data processing module and a data processing module, wherein the Rate-1 outer code error pattern searching module is configured to search the error pattern of the Rate-1 outer code corresponding to the decoding of the polar code serial offset list according to the following processes:
initialization: available error pattern set
Figure BDA0003626064740000038
Unusable sets of error patterns
Figure BDA0003626064740000039
For arbitrary candidate error patterns
Figure BDA00036260647400000310
All have numEp (epsilon) e ) 0; wherein, a l ＝(a l [1],a l [2],...,a l [N v ]) Position coordinates in ascending order of likelihood absolute values representing a sequence of input likelihood values, N v Representing the length of the input sequence of likelihood values; numEp (ε) e ) Is defined as a relation ratio epsilon e The number of small error patterns;
so that the loop variable i is stepped from 1 to log 2 (L), L is the total number of paths, each cycle is i +1, and the method is executed according to the following steps in each cycle:
step 1, selecting an error pattern set
Figure BDA0003626064740000041
Circularly traversing in the set epSet to obtain a candidate error pattern epsilon e ；
Step 2, the sets of error patterns to be compared
Figure BDA0003626064740000042
ε t Representing the error pattern to be compared, and circularly traversing in the set epCompSet to obtain the error pattern epsilon to be compared t ；
Step 3, obtaining the candidate error pattern epsilon e And error pattern epsilon to be compared t Conditional relationship determination to determine whether a relationship exists
Figure BDA0003626064740000043
If yes, executing step 4; if not, executing step 2;
step 4, judging whether epsilon exists t E.g. badSet or epsilon t Epsilon goodSet and numEp (epsilon) t ) Not less than L-1, if yes, executing step 5; if not, numEp (ε) e )＝numEp(ε e ) +1, go to step 2; wherein, numEp (ε) t ) Is defined as a relation ratio epsilon t The number of small error patterns;
step 5, if numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }; completing one cycle;
in the cycle log 2 (L) ending the circulation to obtain all the error patterns epsilon to be selected which satisfy the conditions in each circulation e A set of goodSet; the corresponding set of error patterns is: goodSet { { a { (a) } { (a) } U { (a) } C l [1],a l [2],...,a l [1+log 2 L]}}。
Further, still include: an SPC outer code error pattern search module configured to perform an error pattern search for an SPC outer code corresponding to the PCL CIL decoding according to the following procedure:
initialization: available error pattern set
Figure BDA0003626064740000044
Unusable sets of error patterns
Figure BDA0003626064740000045
For arbitrary candidate error patterns
Figure BDA0003626064740000046
All have numEp (epsilon) e ) 0; wherein, a l ＝(a l [1],a l [2],...,a l [N v ]) Position coordinates in ascending order of likelihood absolute values representing a sequence of input likelihood values, N v Representing the length of the input sequence of likelihood values; numEp (ε) e ) Is defined as a relation ratio epsilon e The number of small error patterns;
so that the cyclic variable i is stepped from 1 to log 2 (L), L is the total number of paths, each cycle is i +1, and the method is executed according to the following steps in each cycle:
step 1, selecting an error pattern set
Figure BDA0003626064740000047
When the parity check value p of the likelihood value hard decision result is 0, circularly traversing in the set epSet to obtain the error pattern epsilon to be selected with the total number of elements of the error pattern to be selected as an even number e (ii) a When the parity check value p of the likelihood value hard decision result is 1, circularly traversing in the set epSet to obtain the error pattern epsilon to be selected with the total number of elements of the error pattern to be selected being odd number e ；
Step 2, the sets of error patterns to be compared
Figure BDA0003626064740000051
ε t Representing the error pattern to be compared, and when the parity value p of the likelihood value hard decision result is equal to 0, circularly traversing in the set epCompSet to obtain the error pattern to be compared epsilon with the total number of elements of the error pattern to be compared being even t (ii) a When the parity check value p of the likelihood value hard decision result is 1, circularly traversing in the set epCompSet to obtain the error graph to be compared with the total number of the elements of the error pattern to be compared being odd numberSample epsilon t ；
Step 3, obtaining the candidate error pattern epsilon e And the error pattern epsilon to be compared t Conditional relationship determination to determine whether a relationship exists
Figure BDA0003626064740000052
If yes, executing step 4; if not, executing step 2;
step 4, judging whether epsilon exists t E.g. badSet or epsilon t E goodSet and numEp (ε) t ) Not less than L-1, if yes, executing step 5; if not, numEp (ε) e )＝numEp(ε e ) +1, executing step 2; wherein, numEp (ε) t ) Is defined as a relation ratio epsilon t The number of small error patterns;
step 5, if numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }; completing one cycle;
in the cycle log 2 (L) ending the circulation to obtain all the error patterns epsilon to be selected which satisfy the conditions in each circulation e A set of goodSet;
if the parity value p is 0, if 1+ log 2 L is an odd number, and the corresponding error pattern set is goodSet; if 1+ log 2 L is an even number, and the corresponding set of error patterns is: goodSet { { a { (a) } { (a) } U { (a) } C l [1],a l [2],...,a l [1+log 2 L]}; if the parity value p is 1, if 1+ log 2 L is an even number, and the corresponding error pattern set is goodSet; if 1+ log 2 L is an odd number, and the corresponding set of error patterns is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}}。
Further, the parity value p represents a modulo-2 sum of all bits of the path input likelihood value sequence hard decision result sequence, and the calculation formula is as follows:
Figure BDA0003626064740000053
wherein alpha is l [i]Representing the input likelihood value sequence alpha corresponding to the ith path l The ith bit of (a), h (·) represents a hard decision function that makes a decision on the input likelihood value sequence corresponding to the current path l;
Figure BDA0003626064740000054
representing modulo-2 addition.
Further, it is determined whether a relationship exists
Figure BDA0003626064740000055
The condition (2) is determined as: satisfy one of the following three conditions
Figure BDA0003626064740000056
If true;
A) if ε t |＝|ε e |，|ε t I denotes the set ε t Number of elements, | epsilon e I denotes the set ε e The number of elements of (1) is then epsilon t The absolute value order of likelihood values corresponding to the mth element in the sequence is less than epsilon e The absolute value order of the likelihood values corresponding to the mth element;
B) if ε t |＜|ε e If need satisfy
Figure BDA0003626064740000061
C) If ε t |＜|ε e If there is an error pattern epsilon k Satisfy the following requirements
Figure BDA0003626064740000062
And is
Figure BDA0003626064740000063
The beneficial technical effects of the invention are as follows:
the invention provides a method and a system for searching an error pattern set related to a polar code serial offset list decoding code word, which are used for searching an error pattern set related to a code word according to different parity check conditions of a Rate-1 outer code or an SPC outer code and according to the input likelihood value sequence length N of the code word v And list size L pairsAnd the limitation of the error pattern generates the required error pattern, so that the error correction capability of the error pattern in the fast serial offset list decoding application can be improved to make up for the loss of the error correction capability.
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The present invention may be better understood by reference to the following description taken in conjunction with the accompanying drawings, which are incorporated in and form a part of this specification, and which are used to further illustrate preferred embodiments of the present invention and to explain the principles and advantages of the present invention.
Fig. 1 is a flowchart of a method for searching an error pattern set associated with a decoded codeword of a polar code serial cancellation list according to an embodiment of the present invention.
FIG. 2 is a graph showing the comparison result of the block error rate simulation of the method of the present invention and the method of reference [4 ].
Detailed Description
In order that those skilled in the art will better understand the disclosure, exemplary embodiments or examples of the disclosure are described below with reference to the accompanying drawings. It is obvious that the described embodiments or examples are only some, but not all embodiments or examples of the invention. All other embodiments or examples obtained by a person of ordinary skill in the art based on the embodiments or examples of the present invention without any creative effort shall fall within the protection scope of the present invention.
The embodiment of the invention provides a method for searching an error pattern set related to a polar code serial offset list decoding code word, which is mainly designed for an error pattern generation process required by a polar code rapid serial offset list decoding algorithm for generating the code word in the decoding process of a Rate-1 and an SPC outer code of the polar code rapid serial offset list decoding algorithm.
The polar code fast serial cancellation list decoding algorithm can be simply divided into two parts of message transmission of a decoding binary tree and decoding of an outer code decoder. The serial cancellation decoding of polar codes itself can be viewed as being log in depth 2 N decoding binary tree, and assuming that the communication channel is additive white Gaussian noiseObtaining the noise variance sigma in combination with the result of the channel estimation 2 The likelihood value sequence corresponding to the receiving vector y can be calculated
Figure BDA0003626064740000071
Likelihood values are transmitted as messages in a binary tree through a specific calculation rule, when a fast serial offset list decoding algorithm traverses to known outer code structures, Rate-1 and SPC, a corresponding decoder needs to calculate a plurality of possible code words, and simultaneously selects L with the highest reliability as output and provides a corresponding likelihood value sequence.
When L paths of the rapid serial offset list decoding algorithm traverse to the Rate-1 or SPC outer code, the input likelihood value sequence corresponding to each path is alpha l ＝(α l [1],α l [2],...,α l [N v ]) In which N is v For the length of the input likelihood value sequence and the subsequent output codeword sequence, the corresponding output codeword sequence is beta l ＝(β l [1],β l [2],...,β l [N v ]). Let a l ＝(a l [1],a l [2],...,a l [N v ]) Ordering the coordinates of the absolute values of the input sequence of likelihood values in ascending order, i.e. a l [i]The likelihood value indicating the ith smaller absolute value of the ith path input likelihood value sequence is at alpha l Wherein i is more than or equal to 1 and less than or equal to N v 。
Chase-II algorithm [4] Four error patterns are selected in the Rate-1 outer code, eight error patterns are selected in the SPC outer code, and the specific result of each codeword is determined by the corresponding error pattern. The input likelihood value sequence length N of two kinds of outer codes is not considered v And the influence of the list size L on its output codeword generation process, so document [4] is adopted]The polar code fast serial cancellation list decoding algorithm of the error pattern generates the loss of error correction capability during decoding. Aiming at the problem, the invention provides a method suitable for different input likelihood value sequence lengths N v And an error pattern set searching method of a list size L, the proposed error pattern can be applied in the generation process of the outer code output code words of Rate-1 and SPC.
First, the input likelihood value sequence of the l path of the Rate-1 or SPC outer code is defined as alpha l ＝(α l [1],α l [2],...,α l [N v ]) The ordered coordinate sequence of the absolute value is a l ＝(a l [1],a l [2],...,a l [N v ]) Wherein a is l [i]Representing the coordinates corresponding to the likelihood value with the ith smaller absolute value of the input likelihood value sequence, i is more than or equal to 1 and less than or equal to N v (ii) a Using f e ＝(f e [1],f e [2],...,f e [N v ]) Indicating the state of the hard decision result for each output codeword bit relative to its input likelihood value when the e-th error pattern is used for the output codeword sequence of the current outer code, if f e [i]0, denotes the corresponding output codeword β l,e [i]＝h(α l [i])，β l,e [i]Indicating the ith bit of the output code word corresponding to the ith error pattern of the ith path; if f is e [i]1, denotes the corresponding output codeword
Figure BDA0003626064740000072
In set theory, one can use
Figure BDA0003626064740000073
Represents { a l [1],a l [2],...,a l [N v ]A set of all subsets of. For example, if N v When 2, then there are
Figure BDA0003626064740000074
Thus, a length of N may be defined from a set perspective v The theoretical error pattern of the outer code is:
ε＝{a l [i]|f e [i]＝1,1≤i≤N v are multiplied by
Figure BDA0003626064740000081
Then, a relation is defined, which acts between two error patterns, writing
Figure BDA0003626064740000082
This relationship holds if one of the following three conditions is satisfied.
A) If ε t |＝|ε e |，ε t The absolute value order of likelihood values corresponding to the m-th element is less than epsilon e The absolute value order of the likelihood values corresponding to the mth element; wherein | ε t Denotes the set ε t Number of elements, | epsilon e I denotes the set ε e The number of the elements is more than or equal to 1 and less than or equal to | epsilon t L. the method is used for the preparation of the medicament. E.g. epsilon t ＝{a l [1],a l [3]}，ε e ＝{a l [2],a l [3]Because the absolute value order of likelihood values corresponding to the first elements of two error patterns has the relation of the condition, there are
Figure BDA0003626064740000083
And
Figure BDA0003626064740000084
B) if ε t |＜|ε e If necessary
Figure BDA0003626064740000085
C) If ε t |＜|ε e If there is an error pattern epsilon k Satisfy the following requirements
Figure BDA0003626064740000086
And is
Figure BDA0003626064740000087
Further, if present
Figure BDA0003626064740000088
Then there is
Figure BDA0003626064740000089
For the outer code of Rate-1 or SPC, the path metric corresponding to the I-th input path is pm l,in If epsilon e The error pattern selected for this purpose has a corresponding output path metric pm l,e Is provided with
Figure BDA00036260647400000810
Then, numEp (ε) is defined e ) Representing the relationship ratio epsilon on the premise of the current outer code e The number of small error patterns; definition numEp (ε) t ) Represents the relation ratio epsilon t The number of small error patterns; defining goodSet for storing available error patterns, wherein the elements of the goodSet are the error patterns of the current outer code; defining badSet for saving unusable error patterns by inputting likelihood value sequence length N v And list size L constraints, such that its corresponding path metric is not selected last, i.e., if epsilon e E.g., badSet, then numEp (ε) e )≥L。
Step one, the search process of the error pattern corresponding to the Rate-1 outer code is as follows:
the initialization is carried out in such a way that,
Figure BDA00036260647400000811
optionally
Figure BDA00036260647400000812
All have numEp (epsilon) e )＝0。
1) The cyclic variable i is stepped from 1 to log 2 (L), go to 2 for each cycle), and go to 7 after finishing.
2) Set of candidate error patterns
Figure BDA00036260647400000813
Circularly traversing the candidate error pattern epsilon e The traversal range is epSet, and the loop is turned into 3) every time, and then turned into 1) after the loop is finished.
3) Sets of patterns to be compared for errors
Figure BDA00036260647400000814
Cyclically traversing the error pattern epsilon to be compared t The traversal range is epCompSet, and the loop is turned into 4) every time, and then turned into 6) after the loop is finished.
4) Using the conditions given above to determine the presence or absence of
Figure BDA0003626064740000091
If yes, turning to 5); if not, go to 3).
5) Determine if there is epsilon t E.g. badSet or epsilon t E goodSet and numEp (ε) t ) More than or equal to L-1: if yes, turning to 6); if not, numEp (ε) e )＝numEp(ε e ) +1, shift to 3).
6) If numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ andycotto { epsilon } e }. And 2) is turned on.
7)goodSet＝goodSet∪{{a l [1],a l [2],...,a l [1+log 2 L]}}。
Different from Rate-1, there are two error pattern sets corresponding to SPC, and the error pattern sets respectively correspond to parity-check characteristics of hard decision results corresponding to current path input likelihood values. Let p be the result of the parity check,
Figure BDA0003626064740000092
wherein alpha is l [i]Representing the input likelihood value sequence alpha corresponding to the ith path l The ith bit of (a), h (·) represents a hard decision function that makes a decision on the input likelihood value sequence corresponding to the current path l;
Figure BDA0003626064740000093
which represents a modulo-2 addition of the signals,
Figure BDA0003626064740000094
step two, searching the corresponding error pattern when the SPC outer code is p is 0 as follows:
the initialization is carried out in such a way that,
Figure BDA0003626064740000095
optionally
Figure BDA0003626064740000096
All have numEp (epsilon) e )＝0。
1) The cyclic variable i is stepped from 1 to log 2 (L), go to 2 for each cycle), and go to 7 after finishing.
2) Candidate set of error patterns
Figure BDA0003626064740000097
Cyclically traverse | ε e Candidate error pattern epsilon with even | number e The traversal range is epSet, and the loop is turned into 3) every time, and then turned into 1) after the loop is finished.
3) Sets of patterns to be compared for errors
Figure BDA0003626064740000098
Cyclically traverse | ε t Error pattern epsilon to be compared with | being even number t The traversal range is epCompSet, and the loop is turned into 4) every time, and then turned into 6) after the loop is finished.
4) Using the conditions given above to determine the presence or absence of
Figure BDA0003626064740000099
If yes, turning to 5); if not, go to 3).
5) Determine if there is epsilon t E.g. badSet or epsilon t Epsilon goodSet and numEp (epsilon) t ) More than or equal to L-1: if yes, go to 6); if not, numEp (ε) e )＝numEp(ε e ) +1, go to 3).
6) If numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }. And 2) is turned on.
7) If 1+ log 2 L is even number, goodSet { { a { (a { } g { (g { } g { (g { } g { (a { } g { (g { } g { (g } g { (g } g { (g } g { } g) l [1],a l [2],...,a l [1+log 2 L]}}。
Step three, searching the corresponding error pattern when the SPC outer code is p equal to 1 as follows:
the initialization is carried out in such a way that,
Figure BDA0003626064740000101
optionally
Figure BDA0003626064740000102
All have numEp (epsilon) e )＝0。
1) The cyclic variable i is stepped from 1 to log 2 (L), go to 2 for each cycle), and 7 after completion.
2) Candidate set of error patterns
Figure BDA0003626064740000103
Cyclically traverse | ε e Candidate error pattern epsilon with odd | e The traversal range is epSet, and the loop is turned into 3) every time, and then turned into 1) after the loop is finished.
3) Sets of patterns to be compared for errors
Figure BDA0003626064740000104
Cyclically traverse | ε t Error pattern epsilon to be compared with i being odd number t The traversal range is epCompSet, and the loop is turned into 4) every time, and then turned into 6) after the loop is finished.
4) Using the conditions given above to determine the presence or absence of
Figure BDA0003626064740000105
If yes, turning to 5); if not, go to 3).
5) Determine if there is epsilon t E.g. badSet or epsilon t E goodSet and numEp (ε) t ) More than or equal to L-1: if yes, turning to 6); if not, numEp (ε) e )＝numEp(ε e ) +1, shift to 3).
6) If numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }. And 2) is turned on.
7) If 1+ log 2 L is an odd number, goodSet ═ goodSet { { a { [ U { { A { [ O ] } is a large number l [1],a l [2],...,a l [1+log 2 L]}}。
The technical effect of the invention is further verified through experiments.
The error pattern obtained by the method of the invention is applied to the generation process of the Rate-1 and SPC outer code output code words corresponding to the quick serial offset list decoding of the polar code, and the simulation result of the decoding block error Rate under different list L sizes is compared with the document [4], as shown in FIG. 2. In the figure, the vertical axis is the block error rate and represents the probability of error of the current transmission sequence; the horizontal axis is the bit signal-to-noise ratio; the dashed line with a plus sign in the figure corresponds to the method of the invention, and the dashed line with a multiplier sign corresponds to the method of document [4 ]. As can be seen from fig. 2, in the decoding of the polar code fast serial cancellation list, the error pattern generated based on the Chase-II algorithm in the document [4] has better error correction performance and lower block error rate.
Another embodiment of the present invention provides a system for searching an error pattern set associated with a code word of a polar code serial cancellation list decoding, including:
the device comprises a Rate-1 outer code error pattern searching module, a data processing module and a data processing module, wherein the Rate-1 outer code error pattern searching module is configured to search the error pattern of the Rate-1 outer code corresponding to the decoding of the polar code serial offset list according to the following processes:
initialization: available error pattern set
Figure BDA0003626064740000106
Unusable sets of error patterns
Figure BDA0003626064740000107
For arbitrary candidate error patterns
Figure BDA0003626064740000108
All have numEp (epsilon) e ) 0; wherein, a l ＝(a l [1],a l [2],...,a l [N v ]) Position coordinates in ascending order of likelihood absolute values representing a sequence of input likelihood values, N v Representing the length of the input sequence of likelihood values; numEp (ε) e ) Is defined as a relation ratio epsilon e The number of small error patterns;
so that the cyclic variable i is stepped from 1 to log 2 (L), L is the total number of paths, each cycle is i +1, and the method is executed according to the following steps in each cycle:
step 1, selecting an error pattern set
Figure BDA0003626064740000111
Circularly traversing in the set epSet to obtain a candidate error pattern epsilon e ；
Step 2, the sets of error patterns to be compared
Figure BDA0003626064740000112
ε t Representing the error pattern to be compared, and circularly traversing in the set epCompSet to obtain the error pattern epsilon to be compared t ；
Step 3, obtaining the candidate error pattern epsilon e And error pattern epsilon to be compared t Conditional relationship determination to determine whether a relationship exists
Figure BDA0003626064740000113
If yes, executing step 4; if not, executing step 2;
step 4, judging whether epsilon exists t E.g. badSet or epsilon t E goodSet and numEp (ε) t ) Not less than L-1, if yes, executing step 5; if not, numEp (ε) e )＝numEp(ε e ) +1, go to step 2; wherein, numEp (ε) t ) Is defined as a relation ratio epsilon t The number of small error patterns;
step 5, if numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }; completing one cycle;
in the cycle log 2 (L) ending the circulation to obtain all the error patterns epsilon to be selected which satisfy the conditions in each circulation e A set of goodSet; the corresponding set of error patterns is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}}。
The system also comprises an SPC outer code error pattern searching module which is configured to search the error pattern of the SPC outer code corresponding to the decoding of the polar code serial offset list according to the following processes:
initialization: available error pattern set
Figure BDA0003626064740000114
Unusable sets of error patterns
Figure BDA0003626064740000115
For arbitrary candidate error patterns
Figure BDA0003626064740000116
All have numEp (epsilon) e ) 0; wherein, a l ＝(a l [1],a l [2],...,a l [N v ]) Position coordinates in ascending order of likelihood absolute values representing a sequence of input likelihood values, N v Representing the length of the input sequence of likelihood values; numEp (ε) e ) Is defined as a relation ratio epsilon e The number of small error patterns;
so that the cyclic variable i is stepped from 1 to log 2 (L), L is the total number of paths, each cycle is i +1, and the method is executed according to the following steps in each cycle:
step 1, selecting an error pattern set
Figure BDA0003626064740000117
When the parity check value p of the likelihood value hard decision result is 0, circularly traversing in the set epSet to obtain the error pattern epsilon to be selected with the total number of elements of the error pattern to be selected as an even number e (ii) a When the parity check value p of the likelihood value hard decision result is 1, circularly traversing in the set epSet to obtain the error pattern epsilon to be selected with the total number of elements of the error pattern to be selected being odd number e ；
Step 2, the sets of error patterns to be compared
Figure BDA0003626064740000121
ε t Representing the error pattern to be compared, and when the parity value p of the likelihood value hard decision result is equal to 0, circularly traversing in the set epCompSet to obtain the error pattern to be compared epsilon with the total number of elements of the error pattern to be compared being even t (ii) a When the parity check value p of the likelihood value hard decision result is 1, circularly traversing in the set epCompSet to obtain the error pattern epsilon to be compared, wherein the total number of elements of the error pattern to be compared is odd t ；
Step (ii) of3. For the obtained candidate error pattern epsilon e And error pattern epsilon to be compared t Conditional relationship determination to determine whether a relationship exists
Figure BDA0003626064740000122
If yes, executing step 4; if not, executing step 2;
step 4, judging whether epsilon exists t E.g. badSet or epsilon t E goodSet and numEp (ε) t ) Not less than L-1, if yes, executing step 5; if not, numEp (ε) e )＝numEp(ε e ) +1, go to step 2; wherein, numEp (ε) t ) Is defined as a relation ratio epsilon t The number of small error patterns;
step 5, if numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }; completing one cycle;
in the circulation log 2 (L) ending the circulation to obtain all the error patterns epsilon to be selected which satisfy the conditions in each circulation e A set of goodSet;
if the parity value p is 0, if 1+ log 2 L is an odd number, and the corresponding error pattern set is goodSet; if 1+ log 2 L is an even number, and the corresponding set of error patterns is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}; if the parity value p is 1, if 1+ log 2 L is an even number, and the corresponding error pattern set is goodSet; if 1+ log 2 L is an odd number, and the corresponding set of error patterns is: goodSet { { a { (a) } { (a) } U { (a) } C l [1],a l [2],...,a l [1+log 2 L]}}。
In this embodiment, the parity value p represents a modulo-2 sum of all bits of the path input likelihood value sequence hard decision result sequence, and a calculation formula thereof is as follows:
Figure BDA0003626064740000123
wherein alpha is l [i]Representing input likelihood corresponding to the ith pathSequence of values alpha l The ith bit of (a), h (·) represents a hard decision function that makes a decision on the input likelihood value sequence corresponding to the current path l;
Figure BDA0003626064740000124
representing modulo-2 addition.
In the present embodiment, whether or not a relationship exists is determined
Figure BDA0003626064740000131
The condition (2) is determined as: satisfy one of the following three conditions
Figure BDA0003626064740000132
Establishing;
A) if ε t |＝|ε e |，|ε t I denotes the set ε t Number of elements, | epsilon e I denotes the set ε e The number of elements of (1) is then epsilon t The absolute value order of likelihood values corresponding to the mth element in the sequence is less than epsilon e The absolute value order of the likelihood values corresponding to the mth element;
B) if ε t |＜|ε e If need to satisfy
Figure BDA0003626064740000133
C) If ε t |＜|ε e If there is an error pattern epsilon k Satisfy the following requirements
Figure BDA0003626064740000134
And is
Figure BDA0003626064740000135
The function of the system for searching for an error pattern set related to a decoded codeword of a crc list in this embodiment can be described by the method for searching for an error pattern set related to a decoded codeword of a crc list, so that the detailed description of this embodiment can be referred to the above method embodiments, and is not repeated herein.
While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as described herein. The present invention has been disclosed in an illustrative rather than a restrictive sense, and the scope of the present invention is defined by the appended claims.
The documents cited in the present invention are as follows:
[1]Arikan,Erdal."Channel polarization:A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels."IEEE Transactions on information Theory 55.7(2009):3051-3073.
[2]Presman,Noam,et al."Binary polarization kernels from code decompositions."IEEE Transactions on Information Theory 61.5(2015):2227-2239.
[3]Tal,Ido,and Alexander Vardy."List decoding of polar codes."IEEE Transactions on Information Theory 61.5 (2015):2213-2226.
[4]Hashemi,Seyyed Ali,Carlo Condo,and Warren J.Gross."A fast polar code list decoder architecture based on sphere decoding."IEEE Transactions on Circuits and Systems I:Regular Papers 63.12(2016):2368-2380。

Claims (7)

1. a search method for error pattern sets related to decoding code words of a polar code serial cancellation list is characterized in that for two corresponding external codes of the polar code serial cancellation list decoding: and (3) carrying out error pattern search by the Rate-1 and SPC outer codes according to the following method:
initialization: available error pattern set
Figure FDA0003626064730000011
Unusable sets of error patterns
Figure FDA0003626064730000012
For arbitrary candidate error patterns
Figure FDA0003626064730000013
All have numEp (epsilon) e ) 0; wherein, a l ＝(a l [1],a l [2],...,a l [N v ]) Position coordinates in ascending order of likelihood absolute values representing a sequence of input likelihood values, N v Representing the length of the input likelihood value sequence; numEp (ε) e ) Is defined as a relation ratio epsilon e The number of small error patterns;
so that the loop variable i is stepped from 1 to log 2 (L), L is the total number of paths, each cycle is i +1, and the method is executed according to the following steps in each cycle:
step 1, a candidate error pattern set
Figure FDA0003626064730000014
For the Rate-1 outer code: circularly traversing in the set epSet to obtain a to-be-selected error pattern epsilon e ；
For SPC outer code, when the parity check value p of the likelihood value hard decision result is 0, circularly traversing in the set epSet to obtain the candidate error pattern epsilon with the total number of elements of the candidate error pattern being even number e ；
For SPC outer code, when the parity check value p of the likelihood value hard decision result is 1, circularly traversing in the set epSet to obtain the candidate error pattern epsilon with the total number of elements of the candidate error pattern being odd number e ；
Step 2, the sets of error patterns to be compared
Figure FDA0003626064730000015
ε t Indicating that the error patterns are to be compared,
for the Rate-1 outer code: circularly traversing in the set epCompSet to obtain an error pattern epsilon to be compared t ；
For SPC outer code, when the parity check value p of the likelihood value hard decision result is 0, circularly traversing in the set epCompSet to obtain the error pattern epsilon to be compared, wherein the total number of elements of the error pattern to be compared is even t ；
For SPC outer code, when likelihood value is odd of hard decision resultWhen the even check value p is equal to 1, circularly traversing in the set epCompSet to obtain the error pattern epsilon to be compared, wherein the total number of elements of the error pattern to be compared is odd number t ；
Step 3, obtaining the candidate error pattern epsilon e And the error pattern epsilon to be compared t Conditional relationship determination to determine whether a relationship exists
Figure FDA0003626064730000016
If yes, executing step 4; if not, executing step 2;
step 4, judging whether epsilon exists t E.g. badSet or epsilon t E goodSet and numEp (ε) t ) Not less than L-1, if yes, executing step 5; if not, numEp (ε) e )＝numEp(ε e ) +1, go to step 2; wherein, numEp (ε) t ) Is defined as a relation ratio epsilon t The number of small error patterns;
step 5, if numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }; completing one cycle;
in the cycle log 2 (L) ending the circulation to obtain all the error patterns epsilon to be selected which satisfy the conditions in each circulation e A set of goodSet;
the error pattern set corresponding to the Rate-1 outer code is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}}；
SPC outer code: if the parity value p is 0, if 1+ log 2 L is an odd number, and the corresponding error pattern set is goodSet; if 1+ log 2 L is an even number, and the corresponding set of error patterns is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}}；
SPC outer code: if the parity value p is 1, if 1+ log 2 L is an even number, and the corresponding error pattern set is goodSet; if 1+ log 2 L is an odd number, and the corresponding set of error patterns is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}}。
2. The method as claimed in claim 1, wherein the parity value p represents a modulo-2 sum of all bits of the path input likelihood value sequence hard decision result sequence, and the calculation formula is as follows:
Figure FDA0003626064730000021
wherein alpha is l [i]Representing the input likelihood value sequence alpha corresponding to the ith path l H (·) represents a hard decision function that makes a decision on the input likelihood value sequence corresponding to the current path l;
Figure FDA0003626064730000022
representing modulo-2 addition.
3. The method as claimed in claim 2, wherein the step 2 of determining whether there is a relationship exists
Figure FDA0003626064730000025
The condition of (2) is determined as: satisfy one of the following three conditions
Figure FDA0003626064730000026
If true;
A) if ε t |＝|ε e |，|ε t I denotes the set ε t The number of elements, | epsilon e I denotes the set ε e The number of elements of (b) is then epsilon t The absolute value order of likelihood values corresponding to the mth element in the sequence is less than epsilon e The absolute value order of the likelihood values corresponding to the mth element;
B) if ε t |＜|ε e If need to satisfy
Figure FDA0003626064730000023
C) If ε t |＜|ε e If there is an error pattern epsilon k Satisfy the following requirements
Figure FDA0003626064730000024
And is
Figure FDA0003626064730000027
4. A system for searching a set of error patterns associated with a decoded codeword from a list of polar code series cancellation (pcl), comprising:
the device comprises a Rate-1 outer code error pattern searching module, a data processing module and a data processing module, wherein the Rate-1 outer code error pattern searching module is configured to search the error pattern of the Rate-1 outer code corresponding to the decoding of the polar code serial offset list according to the following processes:
initialization: available error pattern set
Figure FDA0003626064730000031
Unusable sets of error patterns
Figure FDA0003626064730000032
For arbitrary candidate error patterns
Figure FDA0003626064730000033
Are all numEp (ε) e ) 0; wherein, a l ＝(a l [1],a l [2],...,a l [N v ]) Position coordinates in ascending order of likelihood absolute values representing a sequence of input likelihood values, N v Representing the length of the input likelihood value sequence; numEp (ε) e ) Is defined as a relation ratio epsilon e The number of small error patterns;
so that the loop variable i is stepped from 1 to log 2 (L), L is the total number of paths, each cycle is i +1, and the method is executed according to the following steps in each cycle:
step 1, selecting an error pattern set
Figure FDA0003626064730000034
Circularly traversing in the set epSet to obtain a candidate error pattern epsilon e ；
Step 2, the sets of patterns with errors to be compared
Figure FDA0003626064730000035
ε t Representing the error pattern to be compared, and circularly traversing in the set epCompSet to obtain the error pattern epsilon to be compared t ；
Step 3, obtaining the candidate error pattern epsilon e And error pattern epsilon to be compared t Conditional relationship determination to determine whether a relationship exists
Figure FDA0003626064730000039
If yes, executing step 4; if not, executing step 2;
step 4, judging whether epsilon exists t E.g. badSet or epsilon t E goodSet and numEp (ε) t ) Not less than L-1, if yes, executing step 5; if not, numEp (ε) e )＝numEp(ε e ) +1, go to step 2; wherein, numEp (ε) t ) Is defined as a relation ratio epsilon t The number of small error patterns;
step 5, if numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }; completing one cycle;
in the circulation log 2 (L) ending the circulation to obtain all the error patterns epsilon to be selected which satisfy the conditions in each circulation e A set of goodSet; the corresponding set of error patterns is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}}。
5. The syndrome searching system of claim 4, further comprising: an SPC outer code error pattern search module configured to perform an error pattern search for an SPC outer code corresponding to the PCL CIL decoding according to the following procedure:
initialization: available error pattern set
Figure FDA0003626064730000036
Unusable sets of error patterns
Figure FDA0003626064730000037
For arbitrary candidate error patterns
Figure FDA0003626064730000038
All have numEp (epsilon) e ) 0; wherein, a l ＝(a l [1],a l [2],...,a l [N v ]) Position coordinates in ascending order of likelihood absolute values representing a sequence of input likelihood values, N v Representing the length of the input sequence of likelihood values; numEp (ε) e ) Is defined as a relation ratio epsilon e The number of small error patterns;
so that the cyclic variable i is stepped from 1 to log 2 (L), L is the total number of paths, each cycle is i +1, and the method is executed according to the following steps in each cycle:
step 1, selecting an error pattern set
Figure FDA0003626064730000041
When the parity check value p of the likelihood value hard decision result is 0, circularly traversing in the set epSet to obtain the error pattern epsilon to be selected with the total number of elements of the error pattern to be selected as an even number e (ii) a When the parity check value p of the likelihood value hard decision result is 1, circularly traversing in the set epSet to obtain a candidate error pattern epsilon with the total number of elements of the candidate error pattern being odd number e ；
Step 2, the sets of patterns with errors to be compared
Figure FDA0003626064730000042
ε t Representing the error pattern to be compared, and when the parity check value p of the likelihood value hard decision result is 0, circularly traversing in the set epCompSet to obtain the error pattern to be compared with the elements with even number in total numberPattern epsilon t (ii) a When the parity check value p of the likelihood value hard decision result is 1, circularly traversing in the set epCompSet to obtain the error pattern epsilon to be compared, wherein the total number of elements of the error pattern to be compared is odd t ；
Step 3, obtaining the candidate error pattern epsilon e And error pattern epsilon to be compared t Conditional relationship determination to determine whether a relationship exists
Figure FDA0003626064730000043
If yes, executing step 4; if not, executing step 2;
step 4, judging whether epsilon exists t E.g. badSet or epsilon t E goodSet and numEp (ε) t ) Not less than L-1, if yes, executing step 5; if not, numEp (ε) e )＝numEp(ε e ) +1, go to step 2; wherein, numEp (ε) t ) Is defined as a relation ratio epsilon t The number of small error patterns;
step 5, if numEp (ε) e )<L, goodSet ═ godset @ epsilon @ e Else badSet ═ ≡ ∈ ≡ ∈ else e }; completing one cycle;
in the cycle log 2 (L) ending the circulation to obtain all the error patterns epsilon to be selected which satisfy the conditions in each circulation e A set of goodSet;
if the parity value p is 0, if 1+ log 2 L is an odd number, and the corresponding error pattern set is goodSet; if 1+ log 2 L is an even number, and the corresponding set of error patterns is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}; if the parity value p is 1, if 1+ log 2 L is an even number, and the corresponding error pattern set is goodSet; if 1+ log 2 L is an odd number, and the corresponding set of error patterns is: goodSet { { a { [ U { [ a ] l [1],a l [2],...,a l [1+log 2 L]}}。
6. The system of claim 5, wherein the parity value p represents a modulo-2 sum of all bits of the path input likelihood value sequence hard decision result sequence, and is calculated as follows:
Figure FDA0003626064730000051
wherein alpha is l [i]Representing the input likelihood value sequence alpha corresponding to the ith path l The ith bit of (a), h (·) represents a hard decision function that makes a decision on the input likelihood value sequence corresponding to the current path l;
Figure FDA0003626064730000052
representing modulo-2 addition.
7. The PCL decoding code word associated error pattern set searching system of claim 6, wherein determining whether a relationship exists is based on the relationship
Figure FDA0003626064730000055
The condition (2) is determined as: satisfy one of the following three conditions
Figure FDA0003626064730000056
If true;
A) if ε t |＝|ε e |，|ε t Denotes the set ε t Number of elements, | epsilon e I denotes the set ε e The number of elements of (1) is then epsilon t The absolute value order of likelihood values corresponding to the mth element in the sequence is less than epsilon e The absolute value order of the likelihood values corresponding to the mth element;
B) if ε t |＜|ε e If need to satisfy
Figure FDA0003626064730000053
C) If ε t |＜|ε e If there is an error pattern epsilon k Satisfy the following requirements
Figure FDA0003626064730000054
And is
Figure FDA0003626064730000057
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CN111654291A (en) * 2020-07-02 2020-09-11 重庆邮电大学 Quick serial cancellation list decoding algorithm for polar codes based on bit flipping
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CN114285418A (en) * 2021-12-14 2022-04-05 重庆邮电大学 Improved decoding method for polarization code EPC-MS-SCL

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CN108282264A (en) * 2018-01-05 2018-07-13 西安电子科技大学 The polarization code coding method of list algorithm is serially eliminated based on bit reversal
CN113055022A (en) * 2019-12-26 2021-06-29 华为技术有限公司 Parallel soft cancellation decoding method and related device
CN111654291A (en) * 2020-07-02 2020-09-11 重庆邮电大学 Quick serial cancellation list decoding algorithm for polar codes based on bit flipping
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